Neutron Fluctuations

Neutron Fluctuations

by Imre Pazsit, Lenard Pal
Released October 2007
Publisher(s): Elsevier Science
ISBN: 9780080450643

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Book description

The transport of neutrons in a multiplying system is an area of branching processes with a clear formalism. This book presents an account of the mathematical tools used in describing branching processes, which are then used to derive a large number of properties of the neutron distribution in multiplying systems with or without an external source.

In the second part of the book, the theory is applied to the description of the neutron fluctuations in nuclear reactor cores as well as in small samples of fissile material. The question of how to extract information about the system under study is discussed. In particular the measurement of the reactivity of subcritical cores, driven with various Poisson and non-Poisson (pulsed) sources, and the identification of fissile material samples, is illustrated.

The book gives pragmatic information for those planning and executing and evaluating experiments on such systems.

- Gives a complete treatise of the mathematics of branching particle processes, and in particular neutron fluctuations, in a self-contained manner;
- The first monograph containing the theory and application of neutron fluctuations in low power ADS (spallation and pulsed sources);
- Suitable as a tutorial and handbook/reference book for scientists and graduate students;
- One of the authors is the founder of the mathematical theory of neutron fluctuations in zero power systems.

Table of contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Dedication
  6. Inside Front Cover
  7. PREFACE
  8. ACKNOWLEDGEMENT
  9. LIST OF MOST FREQUENTLY USED NOTATIONS
  10. I: Physics of Branching Processes
    1. Chapter 1: BASIC NOTIONS
      1. 1.1 DEFINITIONS
      2. 1.2 EQUATIONS FOR THE GENERATING FUNCTIONS
      3. 1.3 INVESTIGATION OF THE GENERATING FUNCTION EQUATIONS
      4. 1.4 DISCRETE TIME BRANCHING PROCESSES
      5. 1.5 RANDOM TREE AS A BRANCHING PROCESS
      6. 1.6 ILLUSTRATIVE EXAMPLES
    2. Chapter 2: GENERALISATION OF THE PROBLEM
      1. 2.1 JOINT DISTRIBUTION OF PARTICLE NUMBERS AT DIFFERENT TIME INSTANTS
      2. 2.2 BRANCHING PROCESS WITH TWO PARTICLE TYPES
      3. 2.3 EXTINCTION AND SURVIVAL PROBABILITY
    3. Chapter 3: INJECTION OF PARTICLES
      1. 3.1INTRODUCTION
      2. 3.3 LIMIT PROBABILITIES
      3. 3.4 PROBABILITY OF THE PARTICLE NUMBER IN A NEARLY CRITICAL SYSTEM
    4. Chapter 4: SPECIAL PROBABILITIES
      1. 4.1 Preliminaries
      2. 4.2 The Probability of the Number of Absorptions
      3. 4.3 Probability of the Number of Detections
      4. 4.4 Probability of the Number of Renewals
      5. 4.5 Probability of the Number of Multiplications
    5. Chapter 5: OTHER CHARACTERISTIC PROBABILITIES
      1. 5.1 Introduction
      2. 5.2 Distribution Function of the Survival Time
      3. 5.3 Number of Particles Produced by a Particle and Its Progeny
      4. 5.4 Delayed Multiplication of Particles
      5. 5.5 Process with Prompt and Delayed Born Particles
    6. Chapter 6: BRANCHING PROCESSES IN A RANDOMLY VARYING MEDIUM
      1. 6.1 Characterisation of the Medium
      2. 6.2 Description of the Process
      3. 6.3 Factorial Moments, Variances
      4. 6.4 Random Injection of Particles
    7. Chapter 7: ONE-DIMENSIONAL BRANCHING PROCESS
      1. 7.1 Cell Model
      2. 7.2 CONTINUOUS MODEL
  11. II: Neutron Fluctuations
    1. Chapter 8: NEUTRON FLUCTUATIONS IN THE PHASE SPACE: THE PÁL–BELL EQUATION
      1. 8.1 DEFINITIONS
      2. 8.2 DERIVATION OF THE EQUATION
      3. 8.3 EXPECTATION, VARIANCE AND COVARIANCE
      4. 8.4 PÁL-BELL EQUATION IN THE DIFFUSION APPROXIMATION
    2. Chapter 9: REACTIVITY MEASUREMENT METHODS IN TRADITIONAL SYSTEMS
      1. 9.1 PRELIMINARIES
      2. 9.2 FEYNMAN-ALPHA BY THE FORWARD APPROACH
      3. 9.3 FEYNMAN-ALPHA BY THE BACKWARD APPROACH
      4. 9.4 EVALUATION OF THE FEYNMAN-ALPHA MEASUREMENT
      5. 9.5 THE ROSSI-ALPHA METHOD
      6. 9.6 MOGILNER’S ZERO PROBABILITY METHOD
    3. Chapter 10: REACTIVITY MEASUREMENTS IN ACCELERATOR DRIVEN SYSTEMS
      1. 10.1 STEADY SPALLATION SOURCE
      2. 10.2 PULSED POISSON SOURCE WITH FINITE PULSE WIDTH
      3. 10.3 PULSED COMPOUND POISSON SOURCE WITH FINITE WIDTH
      4. 10.4 PERIODIC INSTANTANEOUS PULSES
    4. Chapter 11: THEORY OF MULTIPLICITY IN NUCLEAR SAFEGUARDS
      1. 11.1 NEUTRON AND GAMMA CASCADES
      2. 11.2 BASIC EQUATIONS
      3. 11.3 NEUTRON DISTRIBUTIONS
      4. 11.4 GAMMA PHOTON DISTRIBUTIONS
      5. 11.5 JOINT MOMENTS
      6. 11.6 PRACTICAL APPLICATIONS: OUTLOOK
  12. Appendices
    1. APPENDIX A: ELEMENTS OF THE THEORY OF GENERATING FUNCTIONS
    2. APPENDIX B: SUPPLEMENT TO THE SURVIVAL PROBABILITY
  13. BIBLIOGRAPHY
  14. INDEX

Product information

  • Title: Neutron Fluctuations
  • Author(s): Imre Pazsit, Lenard Pal
  • Release date: October 2007
  • Publisher(s): Elsevier Science
  • ISBN: 9780080450643